Electron diffraction patterns offer the ability to measure the lattice parameters of crystalline materials. A small (<10 nanometer (nm)) focused electron probe can be produced by a transmission electron microscope (“TEM”), and the probe can be positioned in two dimensions to a precision of better than 1 nm. The probe is amenable to being moved quickly (<1 ms) to any position over a large (>1 μm) field of view. For electron-transparent samples, it is therefore possible to produce so-called nanobeam diffraction (“NBD”) patterns from many discrete points in a sample.
NBD patterns have been used in the past to measure strain in crystalline samples. See, e.g., Koji Usuda et al., Strain characterization in SOI and strained-Si on SGOI MOSFET channel using nano-beam electron diffraction (NBD), Materials Science and Engineering: B, Volumes 124-125, 5 Dec. 2005, Pages 143-147. The absolute strain is derived from the measured shift in position of one or more spots in the electron diffraction pattern from the strained crystal relative to the position of the same spots in the electron diffraction pattern from an unstrained crystal. Either manual measurement or semi-automated measurement using image/feature registration techniques have been used to measure the shift in the diffraction spots. But those methods suffer from some significant systematic errors that result from strong changes in the beam intensity distribution that are not due to strain (see the description of dynamical diffraction below). The precision required for some measurements, which can be less than 0.1% strain, is often not attainable with those methods.
The accuracy and precision of the strain measurement can be improved by fitting an entire diffraction pattern from a strained sample with another diffraction pattern from an unstrained sample that is distorted in directions corresponding to the strain vectors. By fitting the entire diffraction pattern instead of just individual spots, the accuracy and precision are improved over the measurement by including the physical constraint that the shifts of higher-index spots in one direction are linearly proportional to the shifts of their lower-index relatives. The stochastic uncertainly is also reduced by fitting all of the diffraction spots, as opposed to only measuring the limited number of spots whose intensity distribution is not changed too much by dynamical diffraction.
The main systematic errors in measuring spot positions from conventional NBD patterns, and therefore in calculating strain within a material, arise from the fact that the diffraction spot intensities and centers of mass are strongly affected by dynamical electron diffraction. A shift in center of mass of a diffraction spot leads to an error in measuring the spot shift, and the variation in spot intensities can lead to errors in fitting a complete diffraction pattern. The dynamical diffraction effect is strongly influenced by the relative beam/crystal orientation and by sample thickness. Relative orientation variations occur because of sample bending, which is common for thin TEM samples, while local variations in sample thickness are virtually unavoidable using common TEM sample preparation techniques.
Precession electron diffraction (“PED”) has been used to reduce the negative effects of dynamical diffraction. See, e.g., R. Vincent, P. A. Midgley, Double conical beam-rocking system for measurement of integrated electron diffraction intensities, Ultramicroscopy, Volume 53, Issue 3, March 1994, Pages 271-282. In PED, the incident electron beam is precessed at a relatively high frequency (10-1000 Hz) through a small (0.2-5 degrees) angle. This precession reduces the visible effects of dynamical diffraction, so that the diffraction patterns are influenced minimally by variations in sample thickness and bending. Additionally, many additional higher-order reflections appear, which are more sensitive to strain than the lower-order reflections, further enhancing the precision of the strain measurement.
Thus, there exists a need for a process for measuring strain in materials with improved precision. There further exists a need for performing such measurements with high spatial resolution to allow other details of a sampled field to be correlated with strain values derived from the same sample area.